A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at$2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix? 1 Answer Aug 9, 2015 $\left(\text{ganola")/("dried fruit}\right) = \frac{3}{2}$Explanation: Suppose a batch of trail mix is made with $\textcolor{w h i t e}{\text{XXXX}}$$g$lb of granola and $\textcolor{w h i t e}{\text{XXXX}}$$f$lb of dried fruit Then the cost to make a batch would be $\textcolor{w h i t e}{\text{XXXX}}$$1 \cdot g + 2 \cdot f = g + 2 f$With a markup of 25% the selling price would be $\textcolor{w h i t e}{\text{XXXX}}$125% or $\frac{5}{4}$of the cost. A batch weights $\textcolor{w h i t e}{\text{XXXX}}$$g + f$lb and at ($1.75)/("lb")

would sell for a total of $\left(1.75\right) \cdot \left(g + f\right)$
or $\frac{7}{4} \cdot \left(g + f\right)$ dollars.

So
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{5}{4} \cdot \left(g + 2 f\right) = \frac{7}{4} \left(g + f\right)$

$\Rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$5 g + 10 f = 7 g + 7 f$

$\Rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$3 f = 2 g$

That is the ratio of dried fruit to granola is $2 : 3$